{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2009:C7RWX7KCFGYNKFE4EPYJUGP44N","short_pith_number":"pith:C7RWX7KC","canonical_record":{"source":{"id":"0911.1602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-09T08:44:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2c2706f2f8e91e8ab36094a7fc23eced97b374957720ffec8319e85da3300b4a","abstract_canon_sha256":"9b2fa7a6fc67d09467f45921f20b73252a1f0b42cc2633efac2c48e6cab3a945"},"schema_version":"1.0"},"canonical_sha256":"17e36bfd4229b0d5149c23f09a19fce36ded3c59aa105702fd67bda2363d2f70","source":{"kind":"arxiv","id":"0911.1602","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1602","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1602v1","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1602","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"C7RWX7KCFGYN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"C7RWX7KCFGYNKFE4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"C7RWX7KC","created_at":"2026-05-18T12:25:58Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2009:C7RWX7KCFGYNKFE4EPYJUGP44N","target":"record","payload":{"canonical_record":{"source":{"id":"0911.1602","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-09T08:44:40Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"2c2706f2f8e91e8ab36094a7fc23eced97b374957720ffec8319e85da3300b4a","abstract_canon_sha256":"9b2fa7a6fc67d09467f45921f20b73252a1f0b42cc2633efac2c48e6cab3a945"},"schema_version":"1.0"},"canonical_sha256":"17e36bfd4229b0d5149c23f09a19fce36ded3c59aa105702fd67bda2363d2f70","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:08:04.614081Z","signature_b64":"7+RGQMNFOnBxFqRI3RXUm6j28Z7lg7nF8KWhYmDPxw1tug8Pgie2sV3wKME07IhI1bzHuPtYD9BZ8Vp1SKh+BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"17e36bfd4229b0d5149c23f09a19fce36ded3c59aa105702fd67bda2363d2f70","last_reissued_at":"2026-05-18T03:08:04.613336Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:08:04.613336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0911.1602","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1LL4Zv+Yj68OJe7nodpqTgRnHSyVHdGQ0+saCQNPi/StffAYv94fvAYeBfDdeGMZReftPy+iN/oAGvHmcXzYDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:50.161558Z"},"content_sha256":"6024e2264484fbb3662c897fec5da65b93a67d60271d2c1eae42cfd0eb23a7a0","schema_version":"1.0","event_id":"sha256:6024e2264484fbb3662c897fec5da65b93a67d60271d2c1eae42cfd0eb23a7a0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2009:C7RWX7KCFGYNKFE4EPYJUGP44N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A note on flat metric connections with antisymmetric torsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DG","authors_text":"Ilka Agricola, Thomas Friedrich","submitted_at":"2009-11-09T08:44:40Z","abstract_excerpt":"In this short note we study flat metric connections with antisymmetric torsion $T \\neq 0$. The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on $S^7$. The latter case is interesting from the viewpoint of $G_2$-structures and we discuss its type in the sense of the Fernandez-Gray classification. Moreover, we investigate flat metric connections of vectorial type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1602","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:08:04Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Yz/Xxg42wMKletKNmMMS0uqAOp2JuoFeFzdapHbKK+KVCxMA/fUyjet3oqT3XFHQ1k9x0IMAxE3oJ7D8efgrCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T02:37:50.162163Z"},"content_sha256":"331e11a2a98ea6d064d6775f6ba67b1d03db8eed55a2f33b0fba08b7304b8c06","schema_version":"1.0","event_id":"sha256:331e11a2a98ea6d064d6775f6ba67b1d03db8eed55a2f33b0fba08b7304b8c06"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/bundle.json","state_url":"https://pith.science/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-30T02:37:50Z","links":{"resolver":"https://pith.science/pith/C7RWX7KCFGYNKFE4EPYJUGP44N","bundle":"https://pith.science/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/bundle.json","state":"https://pith.science/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/C7RWX7KCFGYNKFE4EPYJUGP44N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:C7RWX7KCFGYNKFE4EPYJUGP44N","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"9b2fa7a6fc67d09467f45921f20b73252a1f0b42cc2633efac2c48e6cab3a945","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-09T08:44:40Z","title_canon_sha256":"2c2706f2f8e91e8ab36094a7fc23eced97b374957720ffec8319e85da3300b4a"},"schema_version":"1.0","source":{"id":"0911.1602","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0911.1602","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"arxiv_version","alias_value":"0911.1602v1","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.1602","created_at":"2026-05-18T03:08:04Z"},{"alias_kind":"pith_short_12","alias_value":"C7RWX7KCFGYN","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_16","alias_value":"C7RWX7KCFGYNKFE4","created_at":"2026-05-18T12:25:58Z"},{"alias_kind":"pith_short_8","alias_value":"C7RWX7KC","created_at":"2026-05-18T12:25:58Z"}],"graph_snapshots":[{"event_id":"sha256:331e11a2a98ea6d064d6775f6ba67b1d03db8eed55a2f33b0fba08b7304b8c06","target":"graph","created_at":"2026-05-18T03:08:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"In this short note we study flat metric connections with antisymmetric torsion $T \\neq 0$. The result has been originally discovered by Cartan/Schouten in 1926 and we provide a new proof not depending on the classification of symmetric spaces. Any space of that type splits and the irreducible factors are compact simple Lie group or a special connection on $S^7$. The latter case is interesting from the viewpoint of $G_2$-structures and we discuss its type in the sense of the Fernandez-Gray classification. Moreover, we investigate flat metric connections of vectorial type.","authors_text":"Ilka Agricola, Thomas Friedrich","cross_cats":["math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-09T08:44:40Z","title":"A note on flat metric connections with antisymmetric torsion"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.1602","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6024e2264484fbb3662c897fec5da65b93a67d60271d2c1eae42cfd0eb23a7a0","target":"record","created_at":"2026-05-18T03:08:04Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"9b2fa7a6fc67d09467f45921f20b73252a1f0b42cc2633efac2c48e6cab3a945","cross_cats_sorted":["math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2009-11-09T08:44:40Z","title_canon_sha256":"2c2706f2f8e91e8ab36094a7fc23eced97b374957720ffec8319e85da3300b4a"},"schema_version":"1.0","source":{"id":"0911.1602","kind":"arxiv","version":1}},"canonical_sha256":"17e36bfd4229b0d5149c23f09a19fce36ded3c59aa105702fd67bda2363d2f70","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"17e36bfd4229b0d5149c23f09a19fce36ded3c59aa105702fd67bda2363d2f70","first_computed_at":"2026-05-18T03:08:04.613336Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:08:04.613336Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7+RGQMNFOnBxFqRI3RXUm6j28Z7lg7nF8KWhYmDPxw1tug8Pgie2sV3wKME07IhI1bzHuPtYD9BZ8Vp1SKh+BA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:08:04.614081Z","signed_message":"canonical_sha256_bytes"},"source_id":"0911.1602","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6024e2264484fbb3662c897fec5da65b93a67d60271d2c1eae42cfd0eb23a7a0","sha256:331e11a2a98ea6d064d6775f6ba67b1d03db8eed55a2f33b0fba08b7304b8c06"],"state_sha256":"2ae8d1df40755f1100282e91b3e11d1abeba1e75f1df367ee90db74678326472"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZnyRxUMuoBuBEzkpvw0OFA8NdkGShJWofDfysX8lY4MEzAuEqvzG3D0IZnwQS//Q51HPGrIbbaDf+iGqOF8DCw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T02:37:50.165243Z","bundle_sha256":"533479c10d9e7219615b95b9b08bbaa48c73cbfa6fcc648ba840d3e1150871e4"}}